Krumm is a short river on the edge of the Swabian Jura of about thirteen kilometers in length. It originates at the base of the Rechberg near the Fuchshof in Rechberg, south of Schwäbisch Gmünd. From there the river makes its way through Ottenbach and Krummwälden up to its confluence with the Fils near Eislingen. The hamlet Krummwälden, which was called in former times as "Welden," carried for some time the name of this river. It was changed to avoid ambiguity.

Krum's dynasty (Bulgarian: Крумова династия) refers to the royal and later imperial family founded by the Khan of Bulgaria Krum (r. 803–814), producing the monarchs of First Bulgarian Empire between 803 and 991. During this period Bulgaria adopted Christianity, reached its greatest territorial extend and a golden age of culture and literature. Under the patronage of these monarch Bulgaria became the birthplace of the Cyrillic alphabet; old Bulgarian became the lingua franca of much of Eastern Europe and it came to be known as Old Church Slavonic. As a result of the victory in the Byzantine–Bulgarian war of 913–927 the Byzantine Empire recognized the imperial title of the Bulgarian rulers and the Bulgarian Orthodox Church as an independent Patriarchate.The last representative of the dynasty, Tsar Roman (r. 977-991), was succeeded by Tsar Samuel (r. 997–1014) of the Cometopuli dynasty, upon his death in Byzantine captivity in 997, after spending six years in prison. Samuel had made the last member of Krum's dynasty a nominal head of state in 977, in order to avoid conflict.

Krumen

Krum Sirakov (Bulgarian: Крум Сираков) or Krum (Bulgarian: Крум) (born in Sofia on 15 August 1986) is a Bulgarian pop and pop-folk singer.

Krum may refer to:

Krum, Haskovo Province is a village in the municipality of Dimitrovgrad, in Haskovo Province, in southern Bulgaria.

Krum Ivanov Yanev

Krummenau (Hunsrück)

Krumau an der Moldau

Krumme Fohre

Building a bright future on a proud past

Krumbach is a river of Bavaria, Germany. It is a left tributary of the Kammel in the town Krumbach.

Krull domain

Krum Ivanov Georgiev (Bulgarian: Крум Иванов Георгиев) (born May 24, 1958) is a Bulgarian chess grandmaster, born in Pazardzhik. He beat Garry Kasparov in a wild game in Malta, 1980.Georgiev earned the International Master (IM) title in 1977 and the Grandmaster (GM) title in 1988.

Krummenau

Krummbek is a municipality in the district of Plön, in Schleswig-Holstein, Germany.

Krull (video game)

Krumhermersdorf

Krumdiack Homestead (also known as the Cook Property) is located on the northern coast of Waldron Island, Washington between Fishery Point and Point Hammond.It was built in 1890 by Friedrich Krumdiak. The site was added to the National Register of Historic Places in 1993.

Krummel

In mathematics, and more specifically in ring theory, Krull's theorem, named after Wolfgang Krull, asserts that a nonzero ring has at least one maximal ideal. The theorem was proved in 1929 by Krull, who used transfinite induction. The theorem admits a simple proof using Zorn's lemma, and in fact is equivalent to Zorn's lemma, which in turn is equivalent to the axiom of choice.

Krummendiek is a municipality in the district of Steinburg, in Schleswig-Holstein, Germany.

Krumovo Air Base

Krulak

Krumm

Krumlovsky Zamek

Krum's dynasty

Krull–Schmidt category

Krummhübel

Krull-Akizuki theorem

Krossblade Aerospace Systems

Krumholtz effect

Krum, TX

Krumovo Gradishte

Krull (comics)

Krummhörn

Krull's intersection theorem

Krummer Woklow is a lake in Mecklenburgische Seenplatte, Mecklenburgische Seenplatte, Mecklenburg-Vorpommern, Germany. At an elevation of 60.5 m, its surface area is 0.42 km².

Krumpendorf am Woerther See

Krumovgrad

Krummbek Manor

Krumdiack Homestead

Krummbach is a river of Baden-Württemberg, Germany. It flows into the Ablach near Meßkirch.

Krumbagel

Krukut River

Krumholz

Krull (disambiguation)

Krumelmonster

Krulj

Krukówka, Podlaskie Voivodeship

Krumbek is a small river of Schleswig-Holstein, Germany. It flows into the Gronau near Ellerau.

Krummholz or krumholtz (German: krumm, "crooked, bent, twisted" and Holz, "wood") — also called knieholz ("knee timber") — is a type of stunted, deformed vegetation encountered in subarctic and subalpine tree line landscapes, shaped by continual exposure to fierce, freezing winds. Under these conditions, trees can only survive where they are sheltered by rock formations or snow cover. As the lower portion of these trees continues to grow, the coverage becomes extremely dense near the ground.

Krummwisch is a municipality in the district of Rendsburg-Eckernförde, in Schleswig-Holstein, Germany.The location of Krummwisch is south of the municipality of Lindau or Schinkel, but north of Bredenbek or Felde, and east of Bovenau.

Krum, tx

Krull's principal ideal theorem

Krumkaker

Krum, Haskovo Province

Krummes Wasser (in its upper course: Hillebach) is a river of Lower Saxony, Germany. It flows into the Ilme in Einbeck.

Krum Yanev

Krumovo (Bulgarian: Крумово) is a village in the Plovdiv Province, southern Bulgaria. As of 2006 it has 3,378 inhabitants. The village is located at 2 km to the south of the Maritsa river and at 12 km to the south-east of Plovdiv. The Plovdiv International Airport is located in the vicinity of the village. It is also famous for its grapes sort Krumovski mavrud. Every 2 years the BIAF Airshow is held on the Krumovo Airbase, resulting in heavy parking problems in the village.

Krumholtz formation

Krum Georgiev Bibishkov

Krullsbach

Krumovitsa River

Krumau (disambiguation)

Krumbach, Austria

Krull's Principal Ideal Theorem

Krum Georgiev Bibishkov (Bulgarian: Крум Георгиев Бибишков; born 2 September 1982 in Marikostinovo, Blagoevgrad Province) is a Bulgarian footballer who currently serves as player-coach for Scarborough SC in the Canadian Soccer League.

Krumovo, Kyustendil Province

Krummhubel

Krumbach Saddle

Krull theorem

Krum Independent School District

Krukówka, Łódź Voivodeship

Krum (Bulgarian: Крум, Greek: Κρούμος/Kroumos) was the Khan of Bulgaria from sometime after 796 but before 803 until his death in 814. During his reign the Bulgarian territory doubled in size, spreading from the middle Danube to the Dnieper and from Odrin to the Tatra Mountains. His able and energetic rule brought law and order to Bulgaria and developed the rudiments of state organization.

Krummennaab

Krull principal ideal theorem

Krumbach, Swabia (district)

Krummesse is a municipality in the district of Lauenburg, in Schleswig-Holstein, Germany.

Kruma

Krummin

Krummbek Manor (German: Herrenhaus Krummbek) is a manor house in the municipality of Lasbek. It is a listed historical monument.

Krumbad

Krumhorn

Krumovgrad (Bulgarian: Крумовград, Turkish: Koşukavak) is a town in Kardzhali Province in the very south of Bulgaria, located in the Eastern Rhodopes on the banks of the river Krumovitsa. The majority of its population is ethnic Turk (70.1%), and with 27.3% ethnic Bulgarian. The town is named after the successful medieval Bulgarian ruler Krum, the name meaning 'city of Krum' in Bulgarian.

Krossen is a village in Mandal municipality in Vest-Agder county, Norway. The village is located in the Mandalen valley, on the western shore of the river Mandalselva, about 10 kilometres (6.2 mi) north of the town of Mandal and about 9 kilometres (5.6 mi) south of the village of Øyslebø.The village (also known as Holum) was the administrative centre of the old municipality of Holum which existed from 1838 until its dissolution in 1964.

Krobanówek

Krummholz

Krukówka

Krossblade Aerospace Systems is an aviation company founded in 2014 in Phoenix, Arizona, USA. The company is known for developing a 5-seat hybrid, vertical take-off and landing, VTOL concept, SkyCruiser, and for its drone/UAV prototype, SkyProwler. Both aircraft employ the switchblade transformation mechanism to transform from a multirotor aircraft for vertical take-off and landing, to a pure winged aircraft, for rapid and efficient cruise.

Krummbach

Krumovo Gradishte is a village in Karnobat Municipality, in Burgas Province, in southeastern Bulgaria.

Krumovo is a village in Aksakovo Municipality, in Varna Province, Bulgaria.

Krummes Wasser

Krumbach Schwaben

Krummer woklow

Kruków, Lower Silesian Voivodeship

Krumbach was a district in Swabia, Bavaria, Germany, before the regional reorganization in 1972. Krumbach was the capital of this district. The licence plate code was KRU.The district had 49 municipalities.

Krummholz or krumholtz (German: krumm, "crooked, bent, twisted" and Holz, "wood") — also called knieholz ("knee timber") — is a type of stunted, deformed vegetation encountered in subarctic and subalpine tree line landscapes, shaped by continual exposure to fierce, freezing winds. Under these conditions, trees can only survive where they are sheltered by rock formations or snow cover. As the lower portion of these trees continues to grow, the coverage becomes extremely dense near the ground. In Newfoundland and Labrador, the formation is known as tuckamore.

Krum (disambiguation)

Krumbach (Kammel)

Krumm (river)

Krull Sharpening

Krumovo is a village in Kocherinovo Municipality, Kyustendil Province, south-western Bulgaria.

Krummel (Westerwald)

Krumbachlein

Krossen

Krum Milev

Krumhermsdorf

Krumsín

Krum Bibishkov

Krumbach

Krummbach (Ablach)

Krumpelmann

Krumme Lanke is a lake in the south west of Berlin, in the Steglitz-Zehlendorf borough of the city and on the edge of the Grunewald forest. After Nikolassee and the neighbouring Schlachtensee, it is the southernmost of the Grunewald chain of lakes.

Krumbächlein

Krummlauf

Krummbach (Dreisam)

Krumm's Pimple

Krummerne, or The Crumbs is a Danish film series about the family Krumborg and particularly the boy 'Krumme' (Laus Høybye). They are loosely based on Thøger Birkeland's popular children's book series that was filmed for the first time. The Crumbs had theatrical release on October 4, 1991, and despite lukewarm reviews the film was a commercial success with over 850,000 cinema admissions.

Krum, Texas

Krumbles

Krulak Mendenhall mission

Krum Ivanov Yanev (9 January 1929 – 24 August 2012) was a Bulgarian footballer who played at both professional and international levels, as a forward.

Gut Krummbek 3

Douglas William Krum, Jr. (born April 27, 1977), who goes by the stage names Krum, formerly he used the stage names Playdough and Harry Krum, is an American hip hop and musician. He's released seven studio albums, one extended play and two mixtapes in his career.

Krull valuation

Krumins

Krummesse

Krumovitsa

Krummel Nuclear Power Plant

Krumbates

Krumbachová

Krueger Airport (FAA LID: OR72) is a private airport located 3 miles (5 km) northeast of Boring in Clackamas County, Oregon, United States. Jeff Linscott purchased the property in 2007 and runs JL Aviation from the airport. The airport faced complaints from neighbors in 2013 over noise from an un-permitted helipad on the property.

Krum Kaka

In commutative algebra, the Krull dimension of a commutative ring R, named after Wolfgang Krull, is the supremum of the lengths of all chains of prime ideals. The Krull dimension need not be finite even for a Noetherian ring. More generally the Krull dimension can be defined for modules over possibly non-commutative rings as the deviation of the poset of submodules.The Krull dimension has been introduced to provide an algebraic definition of the dimension of an algebraic variety: the dimension of the affine variety defined by an ideal I in a polynomial ring R is the Krull dimension of R/I.A field k has Krull dimension 0; more generally, k[x1, ..., xn] has Krull dimension n. A principal ideal domain that is not a field has Krull dimension 1. A local ring has Krull dimension 0 if and only if every element of its maximal ideal is nilpotent.There are several other ways that have been used to define the dimension of a ring. Most of them coincide with the Krull dimension for Noetherian rings, but can differ for non-Noetherian rings.

Krum ISD

Krumovo

Krumkake

Krumbachsattel

Krumm Goes Hollywood

Krukówek

In commutative algebra, the Krull dimension of a commutative ring R, named after Wolfgang Krull, is the supremum of the lengths of all chains of prime ideals. The Krull dimension need not be finite even for a Noetherian ring.

Krullsbach is a river of North Rhine-Westphalia, Germany. It flows into the Lutter northwest of Gütersloh.

Krummholz formation

Krumov Kamak

Krull

Krulevitz, Steve

Krukówko

Krumbz 2 Brickz

Douglas William Krum, Jr.
Krum (rapper)

Krum Kill

The Krumbach Saddle (German: Krumbachsattel, 951 m.) is a high mountain pass in the Austrian Alps in the state of Lower Austria.

Krumberga

Krummenau (Hunsrueck)

Krumbek

Krukut River is a river flowing in Jakarta from a source in Bogor Regency. In the past the river was clean and one of the tourist attractions during the Dutch East Indies administration, but due to denser housing on the banks and lack of maintenance, the water turned dark and filled with trash, causing routine flooding in rainy seasons.

Krummbach (Klosterwaal)

In commutative algebra, a Krull ring or Krull domain is a commutative ring with a well behaved theory of prime factorization. They were introduced by Wolfgang Krull (1931). They are a higher-dimensional generalization of Dedekind domains, which are exactly the Krull domains of dimension at most 1.In this article, a ring is commutative and has unity.

Krumbates was a king of the Chionitae, an ancient tribe of Transoxiana.

Krum is a city in Denton County, Texas, United States. The population was 4,157 at the 2010 census, more than doubling its 2000 census population of 1,984.

Krummennaab is a municipality in the district of Tirschenreuth in Bavaria, Germany.

Krumhermersdorf is a village in the large county borough of Zschopau in the district Erzgebirgskreis in eastern Germany. It was first mentioned in the records in 1369.

Krummerne

Kruków (disambiguation)

Krull–Schmidt theorem

Krumen (disambiguation)

Krueger Airport

Krummnussbaum

Krumen people

Herrenhaus Krummbek

Krummbek

Krumbach was a district in Swabia, Bavaria, Germany, before the regional reorganization in 1972. Krumbach was the capital of this district. The licence plate code was KRU.The district had 49 municipalities. The largest of them were the towns Krumbach, Bavaria and Thannhausen and the municipalities Ziemetshausen, Neuburg an der Kammel and Ursberg.It was bounded by (from the north and clockwise) the districts of Günzburg, Augsburg, Schwabmünchen, Mindelheim, Illertissen and Neu-Ulm.In 1972 the district was merged with Günzburg (district) and the urban district Günzburg to Günzburg district in today's borders.

Krull intersection theorem

Krumovo gradishte

Krumbach (Vorarlberg)

The Krumen (also Kroumen, Kroomen) is an ethnic group living mostly along the coast of Liberia and Côte d’Ivoire. Their numbers were estimated to be 48,300 in 1993, of which 28,300 were in Côte d’Ivoire. They are a subgroup of the Grebo and speak the Krumen language.They are also called Kru, and are related to (but distinct from) the Kru people of the Liberian interior.

Krumme Lanke

Krumbiegel

Krumbach (Swabia)

Krumeich

Krul

Krumlov (disambiguation)

Am Bahnhof 1,Krumhermsdorf,Saxony,

Harry Krum, Playdough

Krumhermsdorf (German: Haltepunkt Krumhermsdorf) is a railway station in the village of Krumhermsdorf, a part of Neustadt in Sachsen, Saxony, Germany. The station lies on the Bautzen–Bad Schandau railway.The station is served by Städtebahn Sachsen. This service connects Pirna and Sebnitz via Neustadt in Sachsen.

Krummsee (Bezirk Kufstein)

The Krummbach is a left tributary of the Dreisam in the Southern Black Forest east of Freiburg im Breisgau in the German state of Baden-Württemberg. It is just under 17 kilometres long, In its upper reaches it is better known as the Zastlerbach; in its middle course it is also known as the Osterbach.

Krumiro

Kruller

Krumen is a dialect continuum spoken by the Krumen people of Liberia and Ivory Coast (Tabou and Grabo subprefectures). It is a branch of the Grebo languages, a subfamily of the Kru languages and ultimately of the Niger–Congo languages. It had 48,300 speakers in 1993.

Krulos

Krumiri Casale Monferrato

Krumholtz

Krumbad is a traditional spa in Swabia, Germany with over 600 years tradition located at the foot of Alps.

Krumiri are a kind of biscuit which is regarded as the particular delicacy of Casale Monferrato, the city in north-west Italy where they were invented in 1878 by the confectioner Domenico Rossi. They are made without water from wheat flour, sugar, butter, eggs and vanilla, in the form of a slightly bent, rough-surfaced cylinder.

Krumm (Fluss)

Krummholz effect

Krump

Krumpendorf am Worther See

Krossen (Kristiansand)

Kruków

Krummendiek

Kronk

Krump battle

Krull schmidt category

23847 Lasbek

Mayor

Krummin is a municipality in the Vorpommern-Greifswald district, in Mecklenburg-Vorpommern, Germany.

Krull's theorem

Kruków, Świętokrzyskie Voivodeship

Krumovgrad, Bulgaria

Krueger Beer

Krull-Remak-Schmidt theorem

Krum dynasty

Krumau

Krumbach (disambiguation)

Krummholtz

Krumbach (Lower Austria)

Krumstedt is a municipality in the district of Dithmarschen, in Schleswig-Holstein, Germany.

Krum Lovkov

Krobanów

Kali Kroekoet, Kali Kruukut, Sungai Krukut

Krumme Lanke is a Berlin U-Bahn station on the U 3. It is the line's southwestern terminus, located in the Zehlendorf district of Berlin.

Krumiri are a kind of biscuit which is regarded as the particular delicacy of Casale Monferrato, the city in north-west Italy where they were invented in 1878 by the confectioner Domenico Rossi. They are made without water from wheat flour, sugar, butter, eggs and vanilla, in the form of a slightly bent, rough-surfaced cylinder. This handlebar shape is said to have been chosen in honour of the extravagantly moustachioed Victor Emanuel II, the first king of united Italy.They may be eaten with—or dunked in—tea, liqueurs, wine, zabaione, etc.

Krossen is a village in Mandal municipality in Vest-Agder county, Norway. The village is located in the Mandalen valley, on the western shore of the river Mandalselva, about 10 kilometres (6.2 mi) north of the town of Mandal and about 9 kilometres (5.6 mi) south of the village of Øyslebø.The village (also known as Holum) was the administrative centre of the old municipality of Holum which existed from 1838 until its dissolution in 1964. Holum Church, built in 1825, is located in Krossen.The 0.48-square-kilometre (120-acre) village has a population (2015) of 610, giving the village a population density of 1,271 inhabitants per square kilometre (3,290/sq mi).

Крумовград

Krum school

Kali Krukut

Krull, Alexander

Krum Georgiev

Krumme Lanke (Berlin U-Bahn)

Krumbo Butte Fire

Krummhuebel

Krummenacher, Victor

Krull is an Atari 2600 video game based on the 1983 science fantasy film Krull and published in 1983 by Atari, Inc. It was written by Dave Staugas who later ported Millipede to the 2600. Gottlieb manufactured an arcade shooter of the same name in the same year, but it is unrelated to the Atari 2600 cartridge other than the Krull license.

Krull-Schmidt theorem

Krummenau (Hunsruck)

Krumkake (Norwegian: [ˈkrʉmˌkɑːkə], meaning bent cake, plural krumkaker) is a Norwegian waffle cookie made of flour, butter, eggs, sugar, and cream. Like the Italian pizzelle, a special decorative two-sided iron griddle, or the Sicilian cannolo, or similar to a waffle iron, is traditionally used to bake the thin round cakes. Older irons are used over the stove, but modern electric irons offer the convenience of nonstick surfaces, automatic timing, and multiple cakes per batch. While hot, the 13–20 cm krumkake are rolled into small cones around a wooden or plastic cone form. Krumkake can be eaten plain or filled with whipped cream (often multekrem) or other fillings.These cookies are popular not only in Norway but also among Norwegian immigrant descendants in New England and the American Midwest. Krumkaker are traditionally made in preparation for Christmas, along with other Norwegian sweets including Sandbakelse and Rosettes. They offer a sweet dessert after the traditional Christmas Eve dinner of ribs or pinnekjøtt.In Germany, the cookies are commonly filled with sweet stuffings. They are also used as a type of ice cream cone.

Krum Lovkov (Bulgarian: Крум Ловков) (born on 19 December 1988) is a Bulgarian footballer currently playing for Brestnik 1948. Lovkov is a defensive midfielder.

Krummwisch

The Krummlauf (English: "curved barrel") is a bent barrel attachment for the Sturmgewehr 44 assault rifle developed by Germany in World War II. The curved barrel included a periscope sighting device for shooting around corners from a safe position.

Kruminiai

Krumlov

Krull's Hauptidealsatz

In commutative algebra, Krull's principal ideal theorem, named after Wolfgang Krull (1899–1971), gives a bound on the height of a principal ideal in a Noetherian ring.

Krumbacher

Krum

Krum Rock

Krukówka (disambiguation)

Krumiri

Krummenau is an Ortsgemeinde – a municipality belonging to a Verbandsgemeinde, a kind of collective municipality – in the Birkenfeld district in Rhineland-Palatinate, Germany. It belongs to the Verbandsgemeinde of Rhaunen, whose seat is in the like-named municipality.

Krumbach (Schwaben)

Krull-Schmidt category

Krum Kill is a stream in the U.S. state of New York."Krum" most likely is derived from Dutch meaning "crooked".

The Krumovitsa (Bulgarian: Крумовица) is a river in the eastern Rhodope Mountains of Bulgaria. The river valley is formed by the Krumovitsa River and the Djushun River together with the surrounding low mountain slopes.

Krummsee (Bezirk Kufstein) is a lake of Tyrol, Austria.

Krulna

Krum Angelov Lovkov

Krumhermsdorf railway station

Krumkake (Norwegian: [ˈkrʉmˌkɑːkə], meaning bent cake, plural krumkaker) is a Norwegian waffle cookie made of flour, butter, eggs, sugar, and cream. Like the Italian pizzelle, a special decorative two-sided iron griddle, or the Sicilian cannolo, or similar to a waffle iron, is traditionally used to bake the thin round cakes. Older irons are used over the stove, but modern electric irons offer the convenience of nonstick surfaces, automatic timing, and multiple cakes per batch.

Krum Milev was a Bulgarian football player and manager. He is often considered as the most successful Bulgarian coach.He played for Botev Sofia, Slavia Sofia and Lokomotiv Sofia.

Krume

Krull–Akizuki theorem

Krulak–Mendenhall mission

Krumen language

Krum Independent School District is a public school district based in Krum, Texas (USA). Located in the growing city of Krum in Denton County, the district serves approximately 1900 students in Denton County and Wise County.Until 2011 Krum was one of the few districts in Texas that did not participate in high-school football, which is extremely rare in Texas.

Krummhorn

Kruminsala

Kroll Associates, Inc.

Krumbein phi scale

Krum (Bulgarian singer)

Krummau

Krummer Woklow

Krum Milev was a Bulgarian football player and manager. He is often considered as the most successful Bulgarian coach.He played for Botev Sofia, Slavia Sofia and Lokomotiv Sofia. He obtained 18 caps with Bulgaria.He was the topscorer of the Bulgarian National Football Division 1937-38.He managed CSKA Sofia, winning the Bulgarian league 11 times with them, Bulgaria, Beroe Stara Zagora and Beşiktaş.Milev holds the record for the longest serving manager (of a single club) in Bulgarian football, having been in charge of CSKA Sofia for 16 years.

Krobar

Krumen is a dialect continuum spoken by the Krumen people of Liberia and Ivory Coast (Tabou and Grabo subprefectures). It is a branch of the Grebo languages, a subfamily of the Kru languages and ultimately of the Niger–Congo languages. It had 48,300 speakers in 1993. The main varieties are:Tepo: Tepo, Bapo, Wlopo / Ropo, Dapo, Honpo, Yrepo / Kapo, Glawlo dialectsPye: Trepo, Wluwe-Hawlo, Gbowe-Hran, Wlepo, Dugbo, Yrewe / Giriwe, Yapo, Pie dialectsPlapoPlapo has only a hundred speakers and no dialectical variation.

Krumm-Heller

Krukt

Krull ring

Krull's Height Theorem

In commutative algebra, Krull's principal ideal theorem, named after Wolfgang Krull (1899–1971), gives a bound on the height of a principal ideal in a Noetherian ring. The theorem is sometimes referred to by its German name, Krulls Hauptidealsatz (Satz meaning "proposition" or "theorem").Formally, if R is a Noetherian ring and I is a principal, proper ideal of R, then I has height at most one.This theorem can be generalized to ideals that are not principal, and the result is often called Krull's height theorem. This says that if R is a Noetherian ring and I is a proper ideal generated by n elements of R, then I has height at most n.The principal ideal theorem and the generalization, the height theorem, both follow from the fundamental theorem of dimension theory. Bourbaki's Commutative Algebra gives a direct proof. Kaplansky's Commutative ring includes a proof due to David Rees.

Krull dimension

Krum (singer)

Krumbein scale

Krum of Bulgaria

Krumovo, Varna Province

Krumstedt

Krum's dynasty (Bulgarian: Крумова династия) refers to the royal and later imperial family founded by the Khan of Bulgaria Krum (r. 803–814), producing the monarchs of First Bulgarian Empire between 803 and 991. During this period Bulgaria adopted Christianity, reached its greatest territorial extend and a golden age of culture and literature.

Krummhoern

Крумово

Krumbein

Krumm, Michael

Krulak-Mendenhall mission

Крум

Krull topology

Krum Independent School District is a public school district based in Krum, Texas (USA). Located in the growing city of Krum in Denton County, the district serves approximately 1900 students in Denton County and Wise County.Until 2011 Krum was one of the few districts in Texas that did not participate in high-school football, which is extremely rare in Texas. A bond election, which would have built a football stadium, was narrowly defeated in November 2006, but was placed on the ballot again in 2007 and was passed. The 2008 school year saw Krum Middle School play the district's first ever football games (defeating the middle school B teams from powerhouse Celina in both the 7th and 8th grade contests). Krum fielded a varsity team in 2011 and played an "outlaw schedule" (i.e., not assigned to a district); the team played its first UIL-sanctioned schedule in 2012 as a member of Class AAA and finished with a 9-1 season.Its boys basketball team has won five state championships (1971, 1978, 1994, 1996, and 1998).In 2011, the school district was rated "recognized" by the Texas Education Agency.

Krosselberg

Heilbad Krumbad GMBH